EXAMPLE 1 Classify direct and inverse variation Tell whether x and y show direct variation, inverse variation, or neither. Given Equation Rewritten Equation Type of Variation y = 7 x a. xy = 7 Inverse b. y = x + 3 Neither y 4 c. = x y = 4x Direct

Write an inverse variation equation EXAMPLE 2 Write an inverse variation equation The variables x and y vary inversely, and y = 7 when x = 4. Write an equation that relates x and y. Then find y when x = –2 . y = a x Write general equation for inverse variation. 7 = a 4 Substitute 7 for y and 4 for x. 28 = a Solve for a. The inverse variation equation is y = 28 x When x = –2, y = –2 = –14. ANSWER

EXAMPLE 3 Write an inverse variation model MP3 Players The number of songs that can be stored on an MP3 player varies inversely with the average size of a song. A certain MP3 player can store 2500 songs when the average size of a song is 4 megabytes (MB). • Write a model that gives the number n of songs that will fit on the MP3 player as a function of the average song size s (in megabytes).

EXAMPLE 3 Write an inverse variation model • Make a table showing the number of songs that will fit on the MP3 player if the average size of a song is 2MB, 2.5MB, 3MB, and 5MB as shown below. What happens to the number of songs as the average song size increases?

Write an inverse variation model EXAMPLE 3 Write an inverse variation model STEP 1 Write an inverse variation model. a n = s Write general equation for inverse variation. a 2500 = 4 Substitute 2500 for n and 4 for s. 10,000 = a Solve for a. A model is n = s 10,000 ANSWER

EXAMPLE 3 Write an inverse variation model STEP 2 Make a table of values. From the table, you can see that the number of songs that will fit on the MP3 player decreases as the average song size increases. ANSWER

GUIDED PRACTICE for Examples 1, 2 and 3 Tell whether x and y show direct variation, inverse variation, or neither. Given Equation Rewritten Equation Type of Variation 1. 3x = y y = 3x Direct y = x 0.75 2. xy = 0.75 Inverse 3. y = x –5 Neither

The inverse variation equation is y = When x = 2, y = 2 = 6. ANSWER GUIDED PRACTICE for Examples 1, 2 and 3 The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 2. 4. x = 4, y = 3 y = a x Write general equation for inverse variation. 4 3 = a Substitute 3 for y and 4 for x. 12 = a Solve for a. 12 x The inverse variation equation is y = When x = 2, y = 2 = 6. ANSWER

The inverse variation equation is y = x When x = 2, y = = – 4. 2 GUIDED PRACTICE for Examples 1, 2 and 3 5. x = 8, y = –1 a y = x Write general equation for inverse variation. –1 = a 8 Substitute – 1 for y and 4 for x. – 8 = a Solve for a. – 8 ANSWER The inverse variation equation is y = x When x = 2, y = = – 4. 2

The inverse variation equation is y = 6 x When x = 2, y = = 3. ANSWER GUIDED PRACTICE for Examples 1, 2 and 3 , 6. x = 1 2 y = 12 y = x a Write general equation for inverse variation. a 12 = 1 2 Substitute 12 for y and for x. 1 2 6 = a Solve for a. The inverse variation equation is y = 6 x When x = 2, y = = 3. ANSWER 2

Write an inverse variation model. GUIDED PRACTICE for Examples 1, 2 and 3 7. What If? In Example 3, what is a model for the MP3 player if it stores 3000 songs when the average song size is 5MB? Write an inverse variation model. n = a s Write general equation for inverse variation. a 3000 = 5 Substitute 3000 for n and 5 for s. 15,000 = a Solve for a. A model is n = s 15,000 ANSWER